Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
/**
 * Created at 18:21 on 2019-09-03
 */

import java.io.*;
import java.util.*;

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long INF = Long.MAX_VALUE / 2;

  static final int e5 = (int) 1e5;

  public static class Solver {

    long[][] comb = new long[51][51];

    public Solver() {

      int N = sc.nextInt();
      int A = sc.nextInt();
      int B = sc.nextInt();

      long[] V = sc.nextLongArray(N, false);

      Array.sort(V);
      V = Array.reverse(V);

      boolean allSame = true;
      long sum = 0;
      for (int i=0; i<A; i++) {
        sum += V[i];
        if (V[i] != V[0]) allSame = false;
      }

      double average = sum / (double)A;

      long sameCountInA = 0;
      long sameCount = 0;
      for (int i=0; i<N; i++) {
        if (V[i] == V[A-1]) {
          sameCount++;
          if (i < A) sameCountInA++;
        }
      }

      long ans = comb(sameCount, sameCountInA);

      if (allSame) {
        for (int i=1; i<=B-A; i++) {
          ans += comb(sameCount, sameCountInA+i);
        }
      }

      out.println(average);
      out.println(ans);

    }

    public long comb(long n, long r) {
      return comb((int)n, (int)r);
    }

    public long comb(int n, int r) {
      if (comb[n][r] != 0) return comb[n][r];
      if (n <= 0 || r < 0 || r > n) return 0;
      if (r == 1) return n;
      return comb[n][r] = comb(n-1, r-1) + comb(n-1, r);
    }

    public static class Array {

      public static void sort(int[] a) {
        shuffle(a);
        Arrays.sort(a);
      }

      public static void sort(long[] a) {
        shuffle(a);
        Arrays.sort(a);
      }

      public static void shuffle(int[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
          int tmp = arr[i];
          int randomPos = i + rnd.nextInt(n-i);
          arr[i] = arr[randomPos];
          arr[randomPos] = tmp;
        }
      }

      public static void shuffle(long[] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
          long tmp = arr[i];
          int randomPos = i + rnd.nextInt(n-i);
          arr[i] = arr[randomPos];
          arr[randomPos] = tmp;
        }
      }

      public static int[] reverse(int[] a) {
        int[] b = new int[a.length];
        for (int i=0; i<a.length; i++) {
          b[a.length-1-i] = a[i];
        }
        return b;
      }

      public static long[] reverse(long[] a) {
        long[] b = new long[a.length];
        for (int i=0; i<a.length; i++) {
          b[a.length-1-i] = a[i];
        }
        return b;
      }

      public static long[] toLong(int[] a) {
        long[] b = new long[a.length];
        for (int i=0; i<a.length; i++) {
          b[i] = a[i];
        }
        return b;
      }

      public static int[] toInt(long[] a) {
        int[] b = new int[a.length];
        for (int i=0; i<a.length; i++) {
          b[i] = (int)a[i];
        }
        return b;
      }

      public static long[] cumulativeSum(int[] a, long mod) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += (b[i-1] + a[i-1]) % mod;
        }
        return b;
      }

      public static long[] cumulativeSum(long[] a, long mod) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += (b[i-1] + a[i-1]) % mod;
        }
        return b;
      }

      public static long[] cumulativeSum(int[] a) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += b[i-1] + a[i-1];
        }
        return b;
      }

      public static long[] cumulativeSum(long[] a) {
        long[] b = new long[a.length+1];
        for(int i=1; i<=a.length; i++) {
          b[i] += b[i-1] + a[i-1];
        }
        return b;
      }

      /*
       * int配列の和を返す
       */
      public static long sum(int[] a) {
        long sum = 0;
        for (int i=0; i<a.length; i++) {
          sum += a[i];
        }
        return sum;
      }

      /*
       * long配列の和を返す
       */
      public static long sum(long[] a) {
        long sum = 0;
        for (int i=0; i<a.length; i++) {
          sum += a[i];
        }
        return sum;
      }

      public static void swap(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
      }

      public static void swap(long[] a, int i, int j) {
        long temp = a[i];
        a[i] = a[j];
        a[j] = temp;
      }

      public static int max(int... a) {
        int M = a[0];
        for (int i = 1; i < a.length; i++) {
          M = Math.max(M, a[i]);
        }
        return M;
      }

      public static int min(int... a) {
        int m = a[0];
        for (int i = 1; i < a.length; i++) {
          m = Math.min(m, a[i]);
        }
        return m;
      }

      public static long max(long... a) {
        long M = a[0];
        for (int i = 1; i < a.length; i++) {
          M = Math.max(M, a[i]);
        }
        return M;
      }

      public static long min(long... a) {
        long m = a[0];
        for (int i = 1; i < a.length; i++) {
          m = Math.min(m, a[i]);
        }
        return m;
      }

      public static int[] iota(int n) {
        int[] a = new int[n];
        for (int i=0; i<n; i++) {
          a[i] = i;
        }
        return a;
      }

      public static long[] iotaL(int n) {
        long[] a = new long[n];
        for (int i=0; i<n; i++) {
          a[i] = i;
        }
        return a;
      }

    }

  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static class FastScanner {
    private InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;


    public void load() {
      try {
        in = new FileInputStream(next());
      } catch (Exception e) {
        e.printStackTrace();
      }
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    private long startTime;

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }

    public void start() {
      startTime = System.currentTimeMillis();
    }

    public void time(String s) {
      long time = System.currentTimeMillis() - startTime;
      println(s + "(" + time + ")");
    }

  }

}